Questions: McKerley Corporation has preferred stock outstanding that will pay an annual dividend of 5.65 per share with the first dividend exactly 15 years from today. If the required return is 3.99 percent, what is the current price of the stock?
Multiple Choice
7874
75.72
13617
81.88
14160
Transcript text: McKerley Corporation has preferred stock outstanding that will pay an annual dividend of $\$ 5.65$ per share with the first dividend exactly 15 years from today. If the required return is 3.99 percent, what is the current price of the stock?
Multiple Choice
$\$ 7874$
$\$ 75.72$
$\$ 13617$
$\$ 81.88$
$\$ 14160$
Solution
Solution Steps
To find the current price of the preferred stock, we need to calculate the present value of the dividend that will be paid in the future. The formula for the present value of a single future payment is:
PV=(1+r)nD
where:
PV is the present value (current price of the stock)
D is the dividend payment (\$5.65)
r is the required return (3.99% or 0.0399)
n is the number of years until the dividend is paid (15 years)
Step 1: Identify the Variables
We are given the following values:
Annual dividend D=5.65
Required return r=0.0399
Number of years until the dividend is paid n=15
Step 2: Calculate the Present Value
To find the current price of the stock, we use the present value formula for a single future payment:
PV=(1+r)nD
Substituting the values into the formula:
PV=(1+0.0399)155.65
Calculating the denominator:
(1+0.0399)15≈1.6653
Now, substituting this back into the present value calculation:
PV≈1.66535.65≈3.1418
Step 3: Round the Result
Rounding the result to four significant digits, we find:
PV≈3.142
Final Answer
The current price of the stock is \\(\boxed{3.14}\\).